Problem: $f(x) = \dfrac{ x + 3 }{ ( x + 3 )( x - 4 ) }$ What is the domain of the real-valued function $f(x)$ ?
$f(x)$ is undefined when the denominator is 0. The denominator is 0 when $x=-3$ or $x=4$ So we know that $x \neq -3$ and $x \neq 4$ Expressing this mathematically, the domain is $\{ \, x \in \RR \mid x \neq-3, \,x \neq4\, \}$.